粗集决策与聚类分析的改进模型

Improved Models of Rough Set Decision-Making and Cluster Analysis

通过分析粗集理论与聚类分析的内在联系,从理论上探讨了两者的融合机理,并给出了相关的数学证明.考虑到粗集决策难以构造决策表的缺陷,采用聚类分析构造等价关系扩展信息表,提出了等价聚类的概念,建立了基于聚类分析的粗集模型;考虑到聚类分析权重确定存在的问题,采用粗集理论的属性约简思想,解决聚类分析中的权重和冗余性问题,建立了基于粗集理论的聚类分析模型,从而解决了原有模型的不足.

By analyzing the intrinsic relationship between the rough set theory and the cluster analysis, their syncretized mechanism was investigated and the correlative mathematical demonstrations were given. Owing to the fact that it is difficult to build a decision table in rough set decision-making, a new concept, equivalent cluster, was put forward by expanding an information table by using the cluster analysis as a tool. As a result, a rough set decision-making model based on the cluster analysis was proposed. In view of the unreasonable determination of weight in the cluster analysis, thinking of attribute reduction in the rough set theory was used to solve the problem of weight determination and redundancy, and a cluster analysis model based on the rough set theory was built so as to overcome the disadvantages of the current rough set decision-making and cluster analysis models.